Stewart was recently revealed to have had a "brief fling" with Sanders, who was her director in Snow White and the Huntsman.
Sanders told People: "I am utterly distraught about the pain I have caused my family.
"My beautiful wife and heavenly children are all I have in this world. I love them with all my heart. I am praying that we can get through this together."
The 41-year-old British director is married to actress-model Liberty Ross, who also appeared in Snow White as Stewart's mother Queen Eleanor.
The couple have two children together.
Stewart, 22, has been dating her Twilight co-star Robert Pattinson, 26, for the last four years.
In a statement released earlier today, Stewart specifically apologised to Pattinson, who she called the person she "loves and respects the most".
Ross is thought to have alluded to the fling on Twitter, where she posted the Marilyn Monroe quote: "Sometimes bad things fall apart so better things can fall together." Ross has since deleted her Twitter account.
Photo gallery - Kristen Stewart and Robert Pattinson's relationship so far:
Copyright: WENNWatch the trailer for Snow White and the Huntsman below: